Fast Spin Echo (FSE) is a well-known NMR technique. A main source of artifacts in FSE is inaccurate phase gradient areas during the echo train. This inaccuracy is generally due to at least one of two factors. One of them is imperfections in the gradient power amplifier. In particular, the gradient power amplifier can produce inaccurate gradient shapes while switching the sign of the current. A second factor, unique to permanent magnet NMR systems, is residual magnetization (RM). The magnetic field gradients produced during the scan can induce a mirror field on the magnet pole pieces that remains for a significant amount of time (at least several minutes) after the gradients are turned off. This RM is approximately linear in space and adapts the field lines of the field gradient. Its actual value is a function of the gradient strength and of the inherent properties of the magnet. While the specific value of this gradient-dependent RM will vary from magnet to magnet, it is typically on the order of 0.1% of the gradient strength, and need only be measured once for any given magnet.
As is known in the art, k=∫0T G(t)dt, where k is a parameter commonly used to represent the k-space in MRI technology, where G(t) is a waveform for gradient pulses (e.g., a trapezoid shaped waveform) and G at a particular time t is the gradient strength (including the proton's gyromagnetic ratio), T is the duration of the gradient pulse. For G in units of Hz mm−1, k is given in units of mm−1. As is known in the art, when G is constant, k can be approximated to be k=GT. Reference is now made to FIG. 1, which illustrates a conventional FSE pulse sequence and gradient pulses, as is known in the art. Phase encoding (pe) along a phase axis Gpe is shown in FIG. 1 with a pattern of a single echo train of having a length ETL. Hereinafter, the subscript and/or superscript pe stands for phase axis or phase encoded axis. For each cycle in the single echo train, two gradients are shown, an encoding gradient kipe, and a reverse gradient that undoes the phase, −kipe.
In order for FSE to work properly, two conditions of the FSE should be met:
(1) At each echo point of the FSE, the phase should vary as ϕ420pe=kipe·rpe, where rpe correspond to a position r along the phase encode axis.
(2) Between two 180° pulses of the FSE, the phase ϕ430pe should be constant. Ideally, ϕ430pe, i.e.ϕ430pe=(k′ipe−kipe)·rpe=0.
Typically, in an NMR/MRI instrument comprising a permanent magnet with pole pieces, neither of the above referenced conditions are fulfilled. Typically, after each encoding gradient kipe, some residual magnetization (RM) gradient is produced. Moreover, due to typical imperfections in the gradient amplifier, the refocusing gradient will not necessarily produce the desired gradient, e.g., a gradient that has an identical shape as the encoding gradient but with opposite sign.
Thus, an FSE pulse sequence that overcomes the aforementioned problems with residual magnetization and that can compensate for imperfections in the gradient amplifier remains a long-felt, yet unmet need.